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Mapping Monday: The Coastline Paradox

Did you know that the coast of the U.S. state of Maine is longer than the coast of California? It is, depending on how you measure it. Measuring a coastline, it turns out, is a complicated matter and can have varying results depending on the method and tools used.

The U.S. state of Maine, as seen in the National Geographic MapMaker Interactive.

Take a look at the coastlines of British Columbia in Canada, Alaska in the United States or Norway in northern Europe. The coastline in these places curves inward and outward everywhere, extrudes into the ocean, become discontinuous at water inlets, and zigzags continuously. It is dotted with bays, coves, and the little inlets that rivers and streams empty into and islands off the coast? When we measure the coastline, do we also include all of these geographic features as part of it? The coastline of the state of Maine is only about 370 kilometers (230 miles) from one end to another. However, when measured taking into consideration its irregularities such as inlets and offshore islands, its length increases to more than 5,542 kilometers (3,450 miles)! It comes to no surprise then that it is counterintuitively difficult to measure the exact length of a coastline.

Even though intuition will tell you that any coastline has a finite length, the length of a coastline depends on the method used to measure it and different methods will give differing answers. For example, the scale of a map will affect the result because at a smaller scale (one that covers a bigger part of the world, like a continent) a coastline will appear to have smaller length than if it has been mapped at a larger scale (covering a smaller part of the world, like a state or province). This is because as we zoom into a region in a map, finer detail emerges and coastlines get increasingly bigger and complex. This apparently counterintuitive observation is fittingly known as the coastline paradox.

There are different ways of representing the curved surface of the Earth on a flat, two-dimensional map. These are mathematical formulae known simply as map projections. The length of a coastline will also vary depending on the type of map projection used, as some projections preserve actual distances while others don’t. For example, the sinusoidal projection preserves distances on lines of latitude, whereas the Mercator projection heavily distorts shapes and distances, especially towards the poles.

The Winkel Tripel projection has been the standard map projection for world maps by the National Geographic Society since 1995. This map projection is preferred because it minimizes the distortion of shape, area, and direction.

The problem of mapping and measuring coastlines is further compounded by the fact that the Earth is a dynamic planet and is changing constantly. An earthquake or meteor collision can trigger a sudden change in the lay of the land that can affect the coastline. Tides–the periodic rise and fall of the sea level that occurs daily due to the gravitational pull of the sun and the moon–can further exacerbate the problem as one coastline can be measured at high tide (when the water extends further into the land surface) while another can be measured at low tide and the results become increasingly convoluted. The tidal range–the vertical difference between high and low tide–can be so great that entire coasts are inundated with water during high tide while the same coasts can become practically dry during low tide (for example, in the Bay of Fundy in Canada). It is virtually impossible to measure a long coastline with exactly the same climatic and geological conditions at every single point.

Photo by Ben Farmer. The incoming tide rushes up the Minas Basin near Wolfville, Nova Scotia, Canada. The Bay of Fundy and its tributaries have the world’s greatest tidal variation, rising and falling twice a day at a normal walking pace.

In recent years emerging geotechnologies like geographic information systems (GIS), which uses software to visualize and manage geographically referenced information including data from global positioning systems (GPS) and remotely sensed imagery, have greatly enhanced our ability to map the coastlines of the world more precisely. However, the coastline paradox will continue to bewilder us all on our quest to become a more geographically literate society.

Written by Neeraj Sirdeshmukh, National Geographic Geography Intern, Winter 2013